{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SPH"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cubic spline kernel function \n",
    "\n",
    "\\begin{equation}\n",
    "W(r,h)=\\frac{C}{{{h}^{d}}}\\left( \\begin{matrix}\n",
    "   1-\\frac{3}{2}{{q}^{2}}+\\frac{3}{4}{{q}^{3}} & {} & 0\\le q<1  \\\\\n",
    "   \\frac{1}{4}{{(2-q)}^{3}} & {} & 1\\le q<2  \\\\\n",
    "   0 & {} & q\\ge 2  \\\\\n",
    "\\end{matrix} \\right. \n",
    "\\end{equation}\n",
    "\n",
    "Where $q=|r|/h$  ,Where C is a scaling factor which assures the compliance with the kernel function properties and depends on the dimension of the problem (e.g. d=1 for 1D):\n",
    "\n",
    "\\begin{equation}\n",
    "C=\\left( \\begin{matrix}\n",
    "   \\frac{2}{3} & d=1  \\\\\n",
    "   \\frac{10}{7\\pi } & d=2  \\\\\n",
    "   \\frac{1}{\\pi } & d=3  \\\\\n",
    "\\end{matrix} \\right.\n",
    "\\end{equation}\n",
    "\n",
    "The 1-order and 2-order derivative of kernal function can be expressed as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "{W}'(r,h)=\\frac{C}{{{h}^{d+1}}}\\left( \\begin{matrix}\n",
    "   -3q+\\frac{9}{4}{{q}^{2}} & 0\\le q<1  \\\\\n",
    "   -\\frac{3}{4}{{(2-q)}^{2}} & 1\\le q<2  \\\\\n",
    "   0 & q\\ge 2  \\\\\n",
    "\\end{matrix} \\right.\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "{W}''(r,h)=\\frac{C}{{{h}^{d+2}}}\\left( \\begin{matrix}\n",
    "   -3+\\frac{9}{2}q & 0\\le q<1  \\\\\n",
    "   \\frac{3}{2}(2-q) & 1\\le q<2  \\\\\n",
    "   0 & q\\ge 2  \\\\\n",
    "\\end{matrix} \\right.\n",
    "\\end{equation}\n",
    "\n",
    "Intergral approximation of 2-order dispersion derivation:\n",
    "$$F({{r}_{i}}-{{r}_{j}})=F(r,h)=\\frac{1}{|r|}{W}'(r,h)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Piecewise function input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline\n",
    "\n",
    "def kernelfun (h, r,d):\n",
    "    q=abs(r/(h**d))\n",
    "    if  d  == 1: C=2/3\n",
    "    elif d == 2: C=10/7/np.pi\n",
    "    elif d == 3: C=1/np.pi\n",
    "    if 0 <= q < 1:\n",
    "        return (1-1.5*q*q+0.75*q*q*q) * C\n",
    "    elif 1 <= q < 2:\n",
    "        return (0.25*(2-q)**3) * C\n",
    "    return 0.0 \n",
    "\n",
    "kfun = np.vectorize(kernelfun)\n",
    "\n",
    "def dkernelfun (h, r,d):\n",
    "    q=abs(r/(h**(d+1)))\n",
    "    if   d == 1: C=2/3\n",
    "    elif d == 2: C=10/7/np.pi\n",
    "    elif d == 3: C=1/np.pi\n",
    "    if 0 <= q < 1:\n",
    "        return (-3*q+2.25*q*q) * C\n",
    "    elif 1 <= q < 2:\n",
    "        return (-0.75*(2-q)**2) * C\n",
    "    return 0.0 \n",
    "\n",
    "dkfun = np.vectorize(dkernelfun)\n",
    "\n",
    "def ddkernelfun (h, r,d):\n",
    "    q=abs(r/(h**(d+2)))\n",
    "    if   d == 1: C=2/3\n",
    "    elif d == 2: C=10/7/np.pi\n",
    "    elif d == 3: C=1/np.pi\n",
    "    if 0 <= q < 1:\n",
    "        return (-3+4.5*q) * C\n",
    "    elif 1 <= q < 2:\n",
    "        return (1.5*(2-q)) * C\n",
    "    return 0.0 \n",
    "\n",
    "ddkfun = np.vectorize(ddkernelfun)\n",
    "\n",
    "def Ffun (h, r,d):\n",
    "    q=abs(r/(h**(d+1)))\n",
    "    if   d == 1: C=2/3\n",
    "    elif d == 2: C=10/7/np.pi\n",
    "    elif d == 3: C=1/np.pi\n",
    "    if 0 <= q < 1:\n",
    "        return (1/abs(r))*(-3*q+2.25*q*q) * C\n",
    "    elif 1 <= q < 2:\n",
    "        return (1/abs(r))*(-0.75*(2-q)**2) * C\n",
    "    return 0.0 \n",
    "\n",
    "Fkfun = np.vectorize(Ffun)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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wqNzJ/ExQZUzlGUBVl6nqOapaS1VrqupZqrq0xDZLVLWSqt4bY//OqrqXqm5LX9TZIbKf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es8n9fK9t4tbHPggvaH06q+wFJ3/3fe9lcJxbov0NZ46/XN7APCUh7TgFuAK1vrGiYi1aNpErXD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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8103400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Four axes, returned as a 2-d array\n",
    "plt.figure(figsize=(16, 16))\n",
    "\n",
    "x = np.linspace(-3, 3, 1000)    \n",
    "y1 = kfun(1, x,1)\n",
    "y2 = dkfun(1, x,1)\n",
    "y3 = ddkfun(1, x,1)\n",
    "y4 = Fkfun(1, x,1)\n",
    "\n",
    "plt.subplot(4, 2, 1)\n",
    "plt.plot(x, y1, '--',lw=2)\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(0, 0.8)\n",
    "plt.grid(True)\n",
    "plt.xlabel('r/h', fontsize=16)\n",
    "plt.ylabel('W(r/h)', fontsize=16)\n",
    "plt.tick_params(labelsize=16)\n",
    "\n",
    "\n",
    "plt.subplot(4, 2, 2)\n",
    "plt.plot(x, y2, '--',lw=2)\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(-0.8, 0.005)\n",
    "plt.grid(True)\n",
    "plt.xlabel('r/h', fontsize=16)\n",
    "plt.ylabel('W prime (r/h)', fontsize=16)\n",
    "plt.tick_params(labelsize=16)\n",
    "\n",
    "\n",
    "plt.subplot(4, 2, 3)\n",
    "plt.plot(x, y3, '--',lw=2)\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(-2, 1)\n",
    "plt.grid(True)\n",
    "plt.xlabel('r/h', fontsize=16)\n",
    "plt.ylabel('dW(r/h)/dr', fontsize=16)\n",
    "plt.tick_params(labelsize=16)\n",
    "\n",
    "\n",
    "plt.subplot(4, 2, 4)\n",
    "plt.plot(x, y4, '--',lw=2)\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(-2, 0.01)\n",
    "plt.grid(True)\n",
    "plt.xlabel('r/h', fontsize=16)\n",
    "plt.ylabel('F(r/h)', fontsize=16)\n",
    "plt.tick_params(labelsize=16)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results in Paulo's paper\n",
    "<img src=\"./resources/kernelfunction.png\" width=\"800\">"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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